A short proof of Eilenberg and Moore’s theorem
In this paper we give a short and simple proof the following theorem of S. Eilenberg and J.C. Moore: the only injective object in the category of groups is the trivial group.
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Maria Nogin (2007)
Open Mathematics
In this paper we give a short and simple proof the following theorem of S. Eilenberg and J.C. Moore: the only injective object in the category of groups is the trivial group.
J. Alejandro Díaz-Barriga, Francisco González-Acuña, Francisco Marmolejo, Leopoldo Román (2004)
Revista Matemática Complutense
Given a generating family F of subgroups of a group G closed under conjugation and with partial order compatible with inclusion, a new group S can be constructed, taking into account the multiplication in the subgroups and their mutual actions given by conjugation. The group S is called the active sum of F, has G as a homomorph and is such that S/Z(S) ≅ G/Z(G) where Z denotes the center.The basic question we investigate in this paper is: when is the active sum S of the family F isomorphic to the...
М.Г. Амаглобели, В.Н. Ремесленников (2000)
Algebra i Logika
М.Г. Амаглобели (2001)
Algebra i Logika
M.Г. Амаглобели (2001)
Algebra i Logika
Luis Ribes (1971)
Mathematische Zeitschrift
José L. Rodríguez, Jérôme Scherer, Lutz Strüngmann (2004)
Fundamenta Mathematicae
As is well known, torsion abelian groups are not preserved by localization functors. However, Libman proved that the cardinality of LT is bounded by whenever T is torsion abelian and L is a localization functor. In this paper we study localizations of torsion abelian groups and investigate new examples. In particular we prove that the structure of LT is determined by the structure of the localization of the primary components of T in many cases. Furthermore, we completely characterize the relationship...
Zvyagina, M.B. (2005)
Zapiski Nauchnykh Seminarov POMI
Florian Pop (1995)
Manuscripta mathematica
Carles Casacuberta, Dirk Scevenels (2001)
RACSAM
Uno de los problemas abiertos más antiguos de la teoría de grupos categórica es si todo par ortogonal (formado por una clase de grupos y una clase de homomorfismos que se determinan mutuamente por ortogonalidad en el sentido de Freyd-Kelly), se halla asociado a un funtor de localización. Se sabe que esto es cierto si se acepta la validez de un cierto axioma de cardinales grandes (el principio de Vopenka), pero no se conoce ninguna demostración mediante los axiomas ordinarios (ZFC) de la teoría de...
Guido Mislin, Peter Hilton (1976)
Mathematische Zeitschrift
Algebra i Logika
Temple H. Fay (1994)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Grundman, H.G., Soltis, D. (2007)
Beiträge zur Algebra und Geometrie
Ayache, Ahmed, Echi, Othman (2005)
International Journal of Mathematics and Mathematical Sciences
Serge Bouc (2015)
Journal of the European Mathematical Society
Let be a prime number. This paper introduces the Roquette category of finite -groups, which is an additive tensor category containing all finite -groups among its objects. In , every finite -group admits a canonical direct summand , called the edge of . Moreover splits uniquely as a direct sum of edges of Roquette -groups, and the tensor structure of can be described in terms of such edges. The main motivation for considering this category is that the additive functors from to...
Zangurashvili, Dali (2003)
Theory and Applications of Categories [electronic only]
Jonathan Leech (1975)
Semigroup forum
Michel Zisman (1977/1978)
Manuscripta mathematica
K.W. Johnson (1974)
Journal für die reine und angewandte Mathematik
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